Partitioning the variation in mammalian substitution rates

We have used analysis of variance to partition the variation in synonymous and amino acid substitution rates between three effects (gene, lineage, and a gene-by-lineage interaction) in mammalian nuclear and mitochondrial genes. We find that gene effects are stronger for amino acid substitution rates than for synonymous substitution rates and that lineage effects are stronger for synonymous substitution rates than for amino acid substitution rates. Gene-by-lineage interactions, equivalent to overdispersion corrected for lineage effects, are found in amino acid substitutions but not in synonymous substitutions. The variance in the ratio of amino acid and synonymous substitution rates is dominated by gene effects, but there is also a significant gene-by-lineage interaction.     

Rate variation among nuclear genes and the age of polyploidy in Gossypium

Molecular evolutionary rate variation in Gossypium (cotton) was characterized using sequence data for 48 nuclear genes from both genomes of allotetraploid cotton, models of its diploid progenitors, and an outgroup. Substitution rates varied widely among the 48 genes, with silent and replacement substitution levels varying from 0.018 to 0.162 and from 0.000 to 0.073, respectively, in comparisons between orthologous Gossypium and outgroup sequences. However, about 90% of the genes had silent substitution rates spanning a more narrow threefold range. Because there was no evidence of rate heterogeneity among lineages for any gene and because rates were highly correlated in independent tests, evolutionary rate is inferred to be a property of each gene or its genetic milieu rather than the clade to which it belongs. Evidence from approximately 200,000 nucleotides (40,000 per genome) suggests that polyploidy in Gossypium led to a modest enhancement in rates of nucleotide substitution. Phylogenetic analysis for each gene yielded the topology expected from organismal history, indicating an absence of gene conversion or recombination among homoeologs subsequent to allopolyploid formation. Using the mean synonymous substitution rate calculated across the 48 genes, allopolyploid cotton is estimated to have formed circa 1.5 million years ago (MYA), after divergence of the diploid progenitors about 6.7 MYA.     

Characterizing the amplitude dynamics of the human core-temperature circadian rhythm using a stochastic-dynamic model

Two measures, amplitude and phase, have been used to describe the characteristics of the endogenous human circadian pacemaker, a biological clock located in the hypothalamus. Although many studies of change in circadian phase with respect to different stimuli have been conducted, the physiologic implications of the amplitude changes (dynamics) of the pacemaker are unknown. It is known that phase changes of the human circadian pacemaker have a significant impact on sleep timing and content, hormone secretion, subjective alertness and neurobehavioral performance. However, the changes in circadian amplitude with respect to different stimuli are less well documented. Although amplitude dynamics of the human circadian pacemaker are observed in physiological rhythms such as plasma cortisol, plasma melatonin and core temperature data, currently methods are not available to accurately characterize the amplitude dynamics from these rhythms. Of the three rhythms core temperature is the only reliable variable that can be monitored continuously in real time with a high sampling rate. To characterize the amplitude dynamics of the circadian pacemaker we propose a stochastic-dynamic model of core temperature data that contains both stochastic and dynamic characteristics. In this model the circadian component that has a dynamic characteristic is represented as a perturbation solution of the van der Pol equation and the thermoregulatory response in the data that has a stochastic characteristic is represented as a first-order autoregressive process. The model parameters are estimated using data with a maximum likelihood procedure and the goodness-of-fit measures along with the associated standard error of the estimated parameters provided inference about the amplitude dynamics of the pacemaker. Using this model we analysed core temperature data from an experiment designed to exhibit amplitude dynamics. We found that the circadian pacemaker recovers slowly to an equilibrium level following amplitude suppression. In humans this reaction to perturbation from equilibrium value has potential physiological implications.     

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of auto-correlated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.     

Examining rates and patterns of nucleotide substitution in plants

Driven by rapid improvements in affordable computing power and by the even faster accumulation of genomic data, the statistical analysis of molecular sequence data has become an active area of interdisciplinary research. Maximum likelihood methods have become mainstream because of their desirable properties and, more importantly, their potential for providing statistically sound solutions in complex data analysis settings. In this chapter, a review of recent literature focusing on rates and patterns of nucleotide substitution rates in the nuclear, chloroplast, and mitochondrial genomes of plants demonstrates the power and flexibility of these new methods. The emerging picture of the nucleotide substitution process in plants is a complex one. Evolutionary rates are seen to be quite variable, both among genes and among plant lineages. However, there are hints, particularly in the chloroplast, that individual factors can have important effects on many genes simultaneously.     

Time-dependent rates of molecular evolution

For over half a century, it has been known that the rate of morphological evolution appears to vary with the time frame of measurement. Rates of microevolutionary change, measured between successive generations, were found to be far higher than rates of macroevolutionary change inferred from the fossil record. More recently, it has been suggested that rates of molecular evolution are also time dependent, with the estimated rate depending on the timescale of measurement. This followed surprising observations that estimates of mutation rates, obtained in studies of pedigrees and laboratory mutation-accumulation lines, exceeded long-term substitution rates by an order of magnitude or more. Although a range of studies have provided evidence for such a pattern, the hypothesis remains relatively contentious. Furthermore, there is ongoing discussion about the factors that can cause molecular rate estimates to be dependent on time. Here we present an overview of our current understanding of time-dependent rates. We provide a summary of the evidence for time-dependent rates in animals, bacteria and viruses. We review the various biological and methodological factors that can cause rates to be time dependent, including the effects of natural selection, calibration errors, model misspecification and other artefacts. We also describe the challenges in calibrating estimates of molecular rates, particularly on the intermediate timescales that are critical for an accurate characterization of time-dependent rates. This has important consequences for the use of molecular-clock methods to estimate timescales of recent evolutionary events.     

The genome as a life-history character: why rate of molecular evolution varies between mammal species

DNA sequences evolve at different rates in different species. This rate variation has been most closely examined in mammals, revealing a large number of characteristics that can shape the rate of molecular evolution. Many of these traits are part of the mammalian life-history continuum: species with small body size, rapid generation turnover, high fecundity and short lifespans tend to have faster rates of molecular evolution. In addition, rate of molecular evolution in mammals might be influenced by behaviour (such as mating system), ecological factors (such as range restriction) and evolutionary history (such as diversification rate). I discuss the evidence for these patterns of rate variation, and the possible explanations of these correlations. I also consider the impact of these systematic patterns of rate variation on the reliability of the molecular date estimates that have been used to suggest a Cretaceous radiation of modern mammals, before the final extinction of the dinosaurs.     

Maximum-likelihood models for combined analyses of multiple sequence data

Models of nucleotide substitution were constructed for combined analyses of heterogeneous sequence data (such as those of multiple genes) from the same set of species. The models account for different aspects of the heterogeneity in the evolutionary process of different genes, such as differences in nucleotide frequencies, in substitution rate bias (for example, the transition/transversion rate bias), and in the extent of rate variation across sites. Model parameters were estimated by maximum likelihood and the likelihood ratio test was used to test hypotheses concerning sequence evolution, such as rate constancy among lineages (the assumption of a molecular clock) and proportionality of branch lengths for different genes. The example data from a segment of the mitochondrial genome of six hominoid species (human, common and pygmy chimpanzees, gorilla, orangutan, and siamang) were analyzed. Nucleotides at the three codon positions in the protein-coding regions and from the tRNA-coding regions were considered heterogeneous data sets. Statistical tests showed that the amount of evolution in the sequence data reflected in the estimated branch lengths can be explained by the codon-position effect and lineage effect of substitution rates. The assumption of a molecular clock could not be rejected when the data were analyzed separately or when the rate variation among sites was ignored. However, significant differences in substitution rate among lineages were found when the data sets were combined and when the rate variation among sites was accounted for in the models. Under the assumption that the orangutan and African apes diverged 13 million years ago, the combined analysis of the sequence data estimated the times for the human-chimpanzee separation and for the separation of the gorilla as 4.3 and 6.8 million years ago, respectively.     

Molecular evolution of the hepatitis B virus genome

The hepatitis B virus (HBV) has a circular DNA genome of about 3,200 base pairs. Economical use of the genome with overlapping reading frames may have led to severe constraints on nucleotide substitutions along the genome and to highly variable rates of substitution among nucleotide sites. Nucleotide sequences from 13 complete HBV genomes were compared to examine such variability of substitution rates among sites and to examine the phylogenetic relationships among the HBV variants. The maximum likelihood method was employed to fit models of DNA sequence evolution that can account for the complexity of the pattern of nucleotide substitution. Comparison of the models suggests that the rates of substitution are different in different genes and codon positions; for example, the third codon position changes at a rate over ten times higher than the second position. Furthermore, substantial variation of substitution rates was detected even after the effects of genes and codon positions were corrected; that is, rates are different at different sites of the same gene or at the same codon position. Such rates after the correction were also found to be positively correlated at adjacent sites, which indicated the existence of conserved and variable domains in the proteins encoded by the viral genome. A multiparameter model validates the earlier finding that the variation in nucleotide conservation is not random around the HBV genome. The test for the existence of a molecular clock suggests that substitution rates are more or less constant among lineages. The phylogenetic relationships among the viral variants were examined. Although the data do not seem to contain sufficient information to resolve the details of the phylogeny, it appears quite certain that the serotypes of the viral variants do not reflect their genetic relatedness. Correspondence to: Z. Yang     

Complex evolution of orthologous and paralogous decarboxylase genes

The decarboxylases are involved in neurotransmitter synthesis in animals, and in pathways of secondary metabolism in plants. Different decarboxylase proteins are characterized for their different substrate specificities, but are encoded by homologous genes. We study, within a maximum-likelihood framework, the evolutionary relationships among dopa decarboxylase (Ddc), histidine decarboxylase (Hdc) and alpha-methyldopa hypersensitive (amd) in animals, and tryptophan decarboxylase (Wdc) and tyrosine decarboxylase (Ydc) in plants. The evolutionary rates are heterogeneous. There are differences between paralogous genes in the same lineages: 4.13 x 10(-10) nucleotide substitutions per site per year in mammalian Ddc vs. 1.95 in Hdc; between orthologous genes in different lineages, 7.62 in dipteran Ddc vs. 4.13 in mammalian Ddc; and very large temporal variations in some lineages, from 3.7 up to 54.9 in the Drosophila Ddc lineage. Our results are inconsistent with the molecular clock hypothesis.     

Testing the molecular clock: molecular and paleontological estimates of divergence times in the Echinoidea (Echinodermata)

The phylogenetic relationships of 46 echinoids, with representatives from 13 of the 14 ordinal-level clades and about 70% of extant families commonly recognized, have been established from 3 genes (3,226 alignable bases) and 119 morphological characters. Morphological and molecular estimates are similar enough to be considered suboptimal estimates of one another, and the combined data provide a tree that, when calibrated against the fossil record, provides paleontological estimates of divergence times and completeness of their fossil record. The order of branching on the cladogram largely agrees with the stratigraphic order of first occurrences and implies that their fossil record is more than 85% complete at family level and at a resolution of 5-Myr time intervals. Molecular estimates of divergence times derived from applying both molecular clock and relaxed molecular clock models are concordant with estimates based on the fossil record in up to 70% of cases, with most concordant results obtained using Sanderson's semiparametric penalized likelihood method and a logarithmic-penalty function. There are 3 regions of the tree where molecular and fossil estimates of divergence time consistently disagree. Comparison with results obtained when molecular divergence dates are estimated from the combined (morphology + gene) tree suggests that errors in phylogenetic reconstruction explain only one of these. In another region the error most likely lies with the paleontological estimates because taxa in this region are demonstrated to have a very poor fossil record. In the third case, morphological and paleontological evidence is much stronger, and the topology for this part of the molecular tree differs from that derived from the combined data. Here the cause of the mismatch is unclear but could be methodological, arising from marked inequality of molecular rates. Overall, the level of agreement reached between these different data and methodological approaches leads us to believe that careful application of likelihood and Bayesian methods to molecular data provides realistic divergence time estimates in the majority of cases (almost 80% in this specific example), thus providing a remarkably well-calibrated phylogeny of a character-rich clade of ubiquitous marine benthic invertebrates.     

Molecular systematics of theDrosophila hydei subgroup as inferred from mitochondrial DNA sequences

The phylogeny of theDrosophila hydei subgroup, which is a member of theD. repleta species group, was inferred from 1,515 base pairs of mitochondrial DNA sequence of the cytochrome oxidase subunits I, II, and III. Four of the seven species in the subgroup were examined, which are placed into two taxonomic complexes: theD. bifurca complex (D. bifurca) andD. nigrohydei) and theD. hydei complex (D. hydei and (D. eohydei). Both complexes appear to be monophyletic, although theD. bifurca complex is only weakly supported. The evolution of chromosomal change, interspecific crossability, sperm gigantism, and divergence times of the subgroup is discussed in a phylogenetic context. Correspondence to: G. Spicer